Multiple Steady-State Solutions for Buoyancy-Induced Transport in Porous Media Saturated with Cold Pure or Saline Water

Abstract

Abstract Vertical laminar buoyancy-induced flows were determined in a porous medium, such as coarse sand, saturated with cold water. Two regions of multiple solutions were found over a range of bounding temperature conditions in terms of a generalized temperature-ratio parameter R. In the range 0 < R < ½, buoyancy force reversals occur across the thermal transport region. This results in flow reversals for some values of R. Further, there is a gap in R where numerical solutions were not found. It can also be shown mathematically that no solutions exist over a subrange of R, consistent with the numerical results. The ranges of R in which multiple solutions do exist are a narrow region below the lower edge of the gap and a wide region above it. In the lower region of multiple solutions, for each value of R, the several solutions found are rather similar. However, in the upper region, the pairs of solutions at the same values of R can be drastically different. One of the two upper-region solutions is largely...